G'day Beatty, welcome to the forum.
Firstly, congratulations on your new property, sounds like you have a nice headstart in making it a great place.
There is an old thread on this topic somewhere I seem to recall which you may like to check out.
As you've already noted, mature trees are great for privacy, shade, windbreak, pollution screen etc, but not that effective for blocking out road noise.
Ideally you could create an earthmound across the front of your property - that is much more effective for noise than a living fence - but from the sounds of things you may not have enough space to make that practical.
Bamboo may well serve better than what you currently have, but you may be disappointed by the fact it doesn't screen out as much noise as you'd hoped. FWIW, there are clumping varieties of bamboo which don't sucker - Bambusa multiplex (Fern leaf bamboo) is one variety I can think of offhand which grows to 3-4 metres and is not invasive...others may have further suggestions for an appropriate species, or you could check out the factsheets at this (click) site...not NZ based but may give you a good guide.
The real path to natural farming requires that a person know what unaltered nature is, so that he or she can instinctively understand what needs to be done—and what must not be done—to work in harmony with its processes. - Masanobu Fukuoka